Problem: Reduce to lowest terms: $- \dfrac{7}{2} \div \dfrac{7}{5} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{7}{5}$ is $ \dfrac{5}{7}$ Therefore: $ - \dfrac{7}{2} \div \dfrac{7}{5} = - \dfrac{7}{2} \times \dfrac{5}{7} $ $ \phantom{- \dfrac{7}{2} \times \dfrac{5}{7}} = \dfrac{-7 \times 5}{2 \times 7} $ $ \phantom{- \dfrac{7}{2} \times \dfrac{5}{7}} = \dfrac{-35}{14} $ The numerator and denominator have a common divisor of $7$, so we can simplify: $ \dfrac{-35}{14} = \dfrac{-35 \div 7}{14 \div 7} = -\dfrac{5}{2} $